Question

If p : switch $S_1$ is closed, q : switch $S_2$ is closed, r : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

• A. p $\wedge$ (q $\vee$ r)
• B. q $\vee$ r
• C. p
• D. ($\sim$ q $\wedge \sim$ r)

Hint:

Series $\to \wedge$ (AND); Parallel $\to \vee$ (OR).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Switches in series correspond to Logical AND ($\wedge$).
Switches in parallel correspond to Logical OR ($\vee$).
Step 2: Key Formula or Approach:
The circuit has a series block containing $S_1$ and a parallel block containing $S_2, S_3$.
Then there is another parallel branch.
Step 3: Detailed Explanation:
Top branch: $p \wedge (q \vee r)$.
Bottom branch: $p \wedge q \wedge r$.
Total: $[p \wedge (q \vee r)] \vee (p \wedge q \wedge r)$.
By distributive law: $p \wedge [(q \vee r) \vee (q \wedge r)] = p \wedge (q \vee r)$.
Step 4: Final Answer:
The form is $p \wedge (q \vee r)$.